Simple heuristics for efficient parallel tensor contraction and quantum circuit simulation

Tensor networks are the main building blocks in a wide variety of computational sciences, ranging from many-body theory and quantum computing to probability and machine learning. Here we propose a parallel algorithm for the contraction of tensor networks using probabilistic graphical models. Our approach is based on the heuristic solution of the $\mu$-treewidth deletion problem in graph theory. We apply the resulting algorithm to the simulation of random quantum circuits and discuss the extensions for general tensor network contractions.